Moments, positive polynomials and their applications
By: Jean-Bernard Lasserre
Series: Imperial College Press optimization series -- v. 1
Publisher: Imperial College Press; Distributed by World Scientific Publishing Co.; World Scientific Publishing Co Pte Ltd
Published: 2010
Place of publication: London; Signapore; Hackensack, NJ
Language: eng
Number of pages: 361
ISBN-13: 9781848164451
Subjects: Mathematical optimization; Moment problems (Mathematics); Algebraic Geometry; Polynomials
Description: "Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application." -- Book cover
Notes: Includes bibliographical references (p. 341-358) and index.